Recall that the freezing point of a solution is *lower* than that of the pure solvent and the ** change in freezing point (ΔT_{f})** is given by:

$\overline{){{\mathbf{\Delta T}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{T}}}_{\mathbf{f}\mathbf{,}\mathbf{}\mathbf{pure}\mathbf{}\mathbf{solvent}}{\mathbf{-}}{{\mathbf{T}}}_{\mathbf{f}\mathbf{,}\mathbf{}\mathbf{solution}}}$

The ** change in freezing point** is also related to the molality of the solution:

$\overline{){{\mathbf{\Delta T}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{imK}}}_{{\mathbf{f}}}}$

where:

**i** = van’t Hoff factor

**m** = molality of the solution (in m or mol/kg)

**K _{f}** = freezing point depression constant (in ˚C/m)

Recall that the ** molality of a solution** is given by:

$\overline{){\mathbf{molality}}{\mathbf{=}}\frac{\mathbf{moles}\mathbf{}\mathbf{solute}}{\mathbf{kg}\mathbf{}\mathbf{solvent}}}$

Using the van't Hoff factors in the table below, calculate the mass of solute required to make each aqueous solution.

Solute | Expected | Measured |

Nonelectrolyte | 1 | 1 |

NaCl | 2 | 1.9 |

MgSO_{4} | 2 | 1.3 |

MgCl_{2} | 3 | 2.7 |

K_{2}SO_{4} | 3 | 2.6 |

FeCl_{3} | 4 | 3.4 |

Calculate the mass of solute required to make a sodium chloride solution containing 161 g of water that has a melting point of -1.9 ^{o}C.

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